Hello,
I know nothing about plants and my supervisor at work gave me a piece of this plant we have standing in the office. I really thought it was a nice plant. Now I have no idea how to take care of it. I'm supposed to re-plant it in something, but don't know what kind of soil to use. So far I've just had it in a cup/glass with a piece of moist paper towel and it's been growing like crazy!!! I thought it would be dead by now. It'd been over two weeks and it's growing and getting more roots, it's even grown a new vine or branch or whatever it is. Now I really do want to repot it before I gets out of hand. It's crawling out of its glass cup now

You have an inch plant, Tradescantia which is one of the easiest plants to grow.

Firstly your cuttings need to be in water, not just on the damp paper towel. I would cut those until you have the leaves with a 3 or 4 inch piece of stem, and put them in the glass half filled with water (change it every few days). In that time your cuttings will have rooted. At that point you can pot them up into a 3 or 4 inch pot - you don't want something too big at first, and use a houseplant compost which you can buy at the store or at a garden centre.

You can pinch out the growing tips as the plant grows, this will keep it bushy.

Good luck and enjoy your plant!

Good info from Sue. Just one comment: If you are in the U.S., what Sue is calling 'potting compost', we call 'potting soil'.

And make sure to put it in a pot that has a hole in the bottom for drainage.

It's an inchplant, Callisia repens:
Inch Plant (Callisia repens)

Very similar habit and culture to creeping Tradescantias.